Unitary reflection groups 1st Edition by Gustav I Lehrer, Donald E Taylor ISBN 0521749891 9780521749893
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Product details:
ISBN 10: 0521749891
ISBN 13: 9780521749893
Author: Gustav I. Lehrer, Donald E. Taylor
A complex reflection is a linear transformation which fixes each point in a hyperplane. Intuitively, it resembles the transformation an image undergoes when it is viewed through a kaleidoscope, or arrangement of mirrors. This book gives a complete classification of all groups of transformations of n-dimensional complex space which are generated by complex reflections, using the method of line systems. In particular: irreducible groups are studied in detail, and are identified with finite linear groups; reflection subgroups of reflection groups are completely classified; the theory of eigenspaces of elements of reflection groups is discussed fully; an appendix outlines links to representation theory, topology and mathematical physics. Containing over 100 exercises ranging in difficulty from elementary to research level, this book is ideal for honors and graduate students, or for researchers in algebra, topology and mathematical physics.
Table of contents:
Chapter 1. Preliminaries
Chapter 2. The Groups G(m,p,n)G(m,p,n)G(m,p,n)
Chapter 3. Polynomial Invariants
Chapter 4. Poincaré Series and Characterisations of Reflection Groups
Chapter 5. Quaternions and the Finite Subgroups of SU(2,C)SU(2, mathbb{C})SU(2,C)
Chapter 6. Finite Unitary Reflection Groups of Rank Two
Chapter 7. Line Systems
Chapter 8. The Shephard and Todd Classification
Chapter 9. The Orbit Map, Harmonic Polynomials, and Semiinvariants
Chapter 10. Covariants and Related Polynomial Identities
Chapter 11. Eigenspace Theory and Reflection Subquotients
Chapter 12. Reflection Cosets and Twisted Invariant Theory
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Tags: Gustav I Lehrer, Donald E Taylor, Unitary, Reflection, Groups